In public sector procurement, social welfare often depends on the time taken to complete the contract. A leading example is highway construction, where slow completion times inflict a negative externality on commuters. Recently, highway departments have introduced innovative contracting methods that give contractors explicit time incentives. We characterize equilibrium bidding and efficient design of these contracts. We then gather a unique data set of highway repair projects awarded by the Minnesota Department of Transportation that includes both innovative and standard contracts. Descriptive analysis shows that for both contract types, contractors respond to the incentives as the theory predicts, both at the bidding stage and after the contract is awarded. Next we build a structural econometric model that endogenizes project completion times, and perform counterfactual policy analysis. Our estimates suggest that switching from standard contracts to designs with socially efficient time incentives would increase welfare by over 19% of the contract value; or in terms of the 2009 Mn/DOT budget, $290 million. We conclude that large improvements in social welfare are possible through the use of improved contract design.